This article considers the conformal mapping of the exterior of the unit disk (the domain |z|>1) onto the exterior (unbounded) domain of a regular triangle. The mapping function is derived using the exterior form of the Christoffel–Schwarz integral, expanded into a power series, and its properties are analysed. It is shown that the logarithmic capacity (conformal radius) of the triangle is expressed through the transcendental constant Γ(1/3): R/C = 2/3 B(2/3,2/3) = 8π²/3Γ(1/3)³ ≈ 1.3689. As a physical application, the ideal fluid flow past the triangle is illustrated. The study employs methods of the geometric theory of functions of a complex variable, the Christoffel–Schwarz integral, series expansion, and computer visualization.
| Mualliflar | Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Kalbaev, Sultanbek Nazerbaevich, Jaksibaev, Sultanbek Amangeldi ulı, Калбаев, Султанбек Назербаевич, Джаксыбаев, Султанбек Амангельдиевич |
|---|---|
| Jurnal | Ilim ha’m ja’miyet |
| Nashr sanasi | 2026-08-15 |
| Son | 5-1 |
| Betlar | 9-11 |
| Til | kaa |
konform akslantirish, Kristoffel-Shvars integrali, muntazam uchburchak, sohaning tashqi ko‘rinishi, logarifmik sig‘im, konform radius, transfinit diametr, gamma-funksiya, kompleks tekislik, ideal suyuqlik oqimi, potensial nazariyasi, конформное отображение, интеграл Кристоффеля–Шварца, правильный треугольник, внешность области, логарифмическая ёмкость, конформный радиус, трансфинитный диаметр, гамма-функция, комплексная плоскость, течение идеальной жидкости, теория потенциала, conformal represcuting, Christoffel–Schwarz integral, regular triangle, exterior domain, logarithmic capacity, conformal radius, transfinite diameter, gamma function, complex plane, ideal fluid flow, potential theory
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